Biophysical techniques that manipulate single molecules provide information on cellular processes such as the remodeling of chromatin and intramolecular structural rearrangements, which bulk assays cannot supply. Thermal fluctuations are important, and statistical theory and modeling that consistently treats the correlation between chemical events and the physical consequences are essential to experimental progress. Specific applications will include: 1) the interpretation of mechanical force-extension measurements on single chromatin fibers in terms of models for the linker histone H1, the effects of salt, and the release/reassembly of the histone octamer due to tension and imposed twist; 2) fluctuations in the linkage connecting the secondary structures, and their binding, and to infer their topology from the order in which they snap; and 3) to explain and provide quantitative predictions for a number of well known morphological features of meiotic chromosomes, using phenomenological methods from polymer statistical mechanics. Green fluorescent chimeric proteins are coming into widespread use as probes to study protein kinesis in the endoplasmic reticulum (ER), Golgi, and endosomal systems in vivo. To interpret experiments that bleach and then image selected regions of the cell with a confocal microscope requires a numerical simulation of diffusion in the inhomogeneous medium defined by the organelle itself. Applications are underway using Golgi and ER markers, to determine their diffusion constants and probe the connectedness of the compartments they occupy. The kinetics of the adsorption of the Golgi by the ER induced by Brefeldin A treatment are not diffusive and a model involving surface tension driven flow is being pursued.